Let \(Y\)  be an Enriques surface. Then \({\rm Num}(Y)\)  is isomorphic to \(E_{10}\) .
If \(Y\)  is of type
I, II, ...or VII, then all \((-2)\) -curves on \(Y\)  appear as vertices of the dual graph and
all genus one fibrations appear as maximal parabolic subdiagrams of the dual graph.
The Enriques' reducibility
lemma (Cossec, Dolgachev and Liedtke [1]}) implies that \((-2)\) -curves on \(Y\)  generate \(E_{10}\) . It follows that effective
irreducible roots on a Coble surface \(S\)  of type I, II, ..., VII generate \(E_{10}\) ,
and hence \({\rm CM}(S)\)  is so.
In case of Coble surface \(S\)  of type MI or MII, consider a parabolic subdiagram
of type \(\tilde{A}_7+\tilde{A}_1\)  or \(\tilde{A}_3+\tilde{A}_3+\tilde{A}_1+\tilde{A}_1\) , respectively,
which defines a special elliptic fibration on \(S\) .
Together with a bi-section it generates a sublattice of \({\rm CM}(S)\)  of finite index whose determinant
is \(-\pm 2^k\) . This implies the assertion.
